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IMO ShortList 2001, algebra problem 4

Source: IMO ShortList 2001, algebra problem 4

September 30, 2004
functionalgebrafunctional equationIMO Shortlist

Problem Statement

Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R}, satisfying f(xy)(f(x)−f(y))=(x−y)f(x)f(y) f(xy)(f(x) - f(y)) = (x-y)f(x)f(y) for all x,yx,y.
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